Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ-type Hamiltonians. (C) 2012 Elsevier B.V. All rights reserved.

Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'.

Two versions of the threshold contact model in two dimensions

Two versions of the threshold contact process ordinary and conservative - are studied on a square lattice. In the first, particles are created on active sites, those having at least two nearest neighbor sites occupied, and are annihilated spontaneously. In the conservative version, a particle jumps from its site to an active site. Mean-field analysis suggests the existence of a first-order phase transition, which is confirmed by Monte Carlo simulations. In the thermodynamic limit, the two versions are found to give the same results. (C) 2012 Elsevier B.V. All rights reserved.

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T, a quantum parameter g, and the ratio p = -J(2)/J(1) where J(1) > 0 refers to ferromagnetic interactions between first-neighbour sites along the d directions of a hypercubic lattice, and J(2) < 0 is associated with competing anti ferromagnetic interactions between second neighbours along m <= d directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g = 0 space, with a Lifshitz point at p = 1/4, for d > 2, and closed-form expressions for the decay of the pair correlations in one dimension. In the T = 0 phase diagram, there is a critical border, g(c) = g(c) (p) for d >= 2, with a singularity at the Lifshitz point if d < (m + 4)/2. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p = 1/4. 2012 (C) Elsevier B.V. All rights reserved.

Stripe-tetragonal phase transition in the two-dimensional Ising model with dipole interactions: Partition function zeros approach

We have performed multicanonical simulations to study the critical behavior of the two-dimensional Ising model with dipole interactions. This study concerns the thermodynamic phase transitions in the range of the interaction delta where the phase characterized by striped configurations of width h = 1 is observed. Controversial results obtained from local update algorithms have been reported for this region, including the claimed existence of a second-order phase transition line that becomes first order above a tricritical point located somewhere between delta = 0.85 and 1. Our analysis relies on the complex partition function zeros obtained with high statistics from multicanonical simulations. Finite size scaling relations for the leading partition function zeros yield critical exponents. that are clearly consistent with a single second-order phase transition line, thus excluding such a tricritical point in that region of the phase diagram. This conclusion is further supported by analysis of the specific heat and susceptibility of the orientational order parameter.

A spatial stochastic model for rumor transmission

We consider an interacting particle system representing the spread of a rumor by agents on the d-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0,1,2}. Here 0 stands for ignorants, 1 for spreaders and 2 for stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate lambda. At rate alpha a spreader becomes a stifler due to the action of other (nearest neighbor) spreaders. Finally, spreaders and stiflers forget the rumor at rate one. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.

The r-matrix of the Alday-Arutyunov-Frolov model

We investigate the classical integrability of the Alday-Arutyunov-Frolov model, and show that the Lax connection can be reduced to a simpler 2 x 2 representation. Based on this result, we calculate the algebra between the L-operators and find that it has a highly non-ultralocal form. We then employ and make a suitable generalization of the regularization technique proposed by Mail let for a simpler class of non-ultralocal models, and find the corresponding r- and s-matrices. We also make a connection between the operator-regularization method proposed earlier for the quantum case, and the Mail let's symmetric limit regularization prescription used for non-ultralocal algebras in the classical theory.

QUASI-TOPOLOGICAL QUANTUM FIELD THEORIES AND Z(2) LATTICE GAUGE THEORIES

We consider a two-parameter family of Z(2) gauge theories on a lattice discretization T(M) of a three-manifold M and its relation to topological field theories. Familiar models such as the spin-gauge model are curves on a parameter space Gamma. We show that there is a region Gamma(0) subset of Gamma where the partition function and the expectation value h < W-R(gamma)> i of the Wilson loop can be exactly computed. Depending on the point of Gamma(0), the model behaves as topological or quasi-topological. The partition function is, up to a scaling factor, a topological number of M. The Wilson loop on the other hand, does not depend on the topology of gamma. However, for a subset of Gamma(0), < W-R(gamma)> depends on the size of gamma and follows a discrete version of an area law. At the zero temperature limit, the spin-gauge model approaches the topological and the quasi-topological regions depending on the sign of the coupling constant.

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.

Annealed Ising model on hierarchical structures: a transfer matrix approach.

Spin systems in the presence of disorder are described by two sets of degrees of freedom, associated with orientational (spin) and disorder variables, which may be characterized by two distinct relaxation times. Disordered spin models have been mostly investigated in the quenched regime, which is the usual situation in solid state physics, and in which the relaxation time of the disorder variables is much larger than the typical measurement times. In this quenched regime, disorder variables are fixed, and only the orientational variables are duly thermalized. Recent studies in the context of lattice statistical models for the phase diagrams of nematic liquid-crystalline systems have stimulated the interest of going beyond the quenched regime. The phase diagrams predicted by these calculations for a simple Maier-Saupe model turn out to be qualitative different from the quenched case if the two sets of degrees of freedom are allowed to reach thermal equilibrium during the experimental time, which is known as the fully annealed regime. In this work, we develop a transfer matrix formalism to investigate annealed disordered Ising models on two hierarchical structures, the diamond hierarchical lattice (DHL) and the Apollonian network (AN). The calculations follow the same steps used for the analysis of simple uniform systems, which amounts to deriving proper recurrence maps for the thermodynamic and magnetic variables in terms of the generations of the construction of the hierarchical structures. In this context, we may consider different kinds of disorder, and different types of ferromagnetic and anti-ferromagnetic interactions. In the present work, we analyze the effects of dilution, which are produced by the removal of some magnetic ions. The system is treated in a “grand canonical" ensemble. The introduction of two extra fields, related to the concentration of two different types of particles, leads to higher-rank transfer matrices as compared with the formalism for the usual uniform models. Preliminary calculations on a DHL indicate that there is a phase transition for a wide range of dilution concentrations. Ising spin systems on the AN are known to be ferromagnetically ordered at all temperatures; in the presence of dilution, however, there are indications of a disordered (paramagnetic) phase at low concentrations of magnetic ions.

Comparison of model potentials for molecular dynamics simulation of crystalline silica

Simulationen von SiO2 mit dem von van Beest, Kramer und vanSanten (BKS) entwickelten Paarpotenzial erzeugen vielezufriedenstellende Ergebnisse, aber auch charakteristischeSchwachstellen. In dieser Arbeit wird das BKS-Potenzial mitzwei kürzlich vorgeschlagenen Potenzialen verglichen, dieeffektiv Mehrteilchen-Wechselwirkungen beinhalten. Der ersteAnsatz erlaubt dazu fluktuierende Ladungen, der zweiteinduzierbare Polarisierungen auf den Sauerstoffatomen. Die untersuchten Schwachstellen des BKS Potenzialsbeinhalten das Verhältnis der zwei Gitterkonstanten a und cim Quarzübergang, das von BKS falsch beschrieben wird.Cristobalit und Tridymit erscheinen instabil mit BKS.Weiterhin zeigt die BKS-Zustandsdichte charakteristischeAbweichungen von der wahren Zustandsdichte. DerÜbergangsdruck für den Stishovit I-II Übergang wird deutlichüberschätzt. Das Fluktuierende-Ladungs-Modell verbesserteinige der genannten Punkte, reproduziert aber viele andereEigenschaften schlechter als BKS. DasFluktierende-Dipol-Modell dagegen behebt alle genanntenArtefakte. Zusätzlich wird der druckinduzierte Phasenübergang imalpha-Quarz untersucht. Alle Potentiale finden die selbeStruktur für Quarz II. Bei anschliessender Dekompressionerzeugt BKS eine weitere Phase, während die beiden anderenPotentiale wieder zum alpha-Quarz zurückkehren. Weiterhinwerden zwei Methoden entwickelt, um die piezoelektrischenKonstanten bei konstantem Druck zu bestimmen. Die Ergebnissegeben Hinweise auf eine möglicherweisenicht-elektrostatische Natur der Polarisierungen imFluktuierende-Dipole-Modell. Mit dieser Interpretation scheint das Fluktuierende-DipolPotential alle verfügbaren experimentellen Daten am bestenvon allen drei untersuchten Ansätzen zu reproduzieren.

Lattice preferred orientation in omphacite: Examples from the Tauern Window, Austria and the Western Gneiss Region, Norway

It is lively debated how eclogites find their way from deep to mid-crustal levels during exhumation. Different exhumation models for high-pressure and ultrahigh-pressure rocks were suggested in previous studies, based mainly on field observations and less on microstructural studies on the exhumed rocks. The development and improvement of electron microscopy techniques allows it, to focus interest on direct investigations of microstructures and crystallographic properties in eclogites. In this case, it is of importance to study the applicability of crystallographic measurements on eclogites for exhumation processes and to unravel which processes affect eclogite textures. Previous studies suggested a strong relationship between deformation and lattice preferred orientation (LPO) in omphacite but it is still unclear if the deformation is related to the exhumation of eclogites. This study is focused on the questions which processes affect omphacite LPO and if textural investigations of omphacite are applicable for studying eclogite exhumation. Therefore, eclogites from two examples in the Alps and in the Caledonides were collected systematically and investigated with respect to omphacite LPO by using the electron backscattered diffraction (EBSD) technique. Omphacite textures of the Tauern Window (Austria) and the Western Gneiss Region (Norway) were studied to compare lattice preferred orientation with field observations and suggested exhumation models from previous studies. The interpretation of omphacite textures, regarding the deformation regime is mainly based on numerical simulations in previous studies. Omphacite LPO patterns of the Eclogite Zone are clearly independent from any kind of exhumation process. The textures were generated during omphacite growth on the prograde path of eclogite development until metamorphic peak conditions. Field observations in the Eclogite Zone show that kinematics in garnet mica schist, surrounding the eclogites, strongly indicate an extrusion wedge geometry. Stretching lineations show top-N thrusting at the base and a top-S normal faulting with a sinistral shear component at the top of the Eclogite Zone. The different shear sense on both sides of the unit does not affect the omphacite textures in any way. The omphacite lattice preferred orientation patterns of the Western Gneiss Region can not be connected with any exhumation model. The textures were probably generated during the metamorphic peak and reflect the change from subduction to exhumation. Eclogite Zone and Western Gneiss Region differ significantly in size and especially in metamorphic conditions. While the Eclogite Zone is characterized by constant P-T conditions (600-650°C, 20-25 kbar), the Western Gneiss Region contains a wide P-T range from high- to ultrahigh pressure conditions (400-800°C, 20-35 kbar). In contrast to this, the omphacite textures of both units are very similar. This means that omphacite LPO is independent from P-T conditions and therefore from burial depth. Further, in both units, omphacite LPO is independent from grain and subgrain size as well as from any shape preferred orientation (SPO) on grain and subgrain scale. Overall, omphacite lattice preferred orientation are generated on the prograde part of omphacite development. Therefore, textural investigations on omphacite LPO are not applicable to study eclogite exhumation.

Fluid-structure interaction by a coupled lattice Boltzmann-finite element approach

In this thesis, a strategy to model the behavior of fluids and their interaction with deformable bodies is proposed. The fluid domain is modeled by using the lattice Boltzmann method, thus analyzing the fluid dynamics by a mesoscopic point of view. It has been proved that the solution provided by this method is equivalent to solve the Navier-Stokes equations for an incompressible flow with a second-order accuracy. Slender elastic structures idealized through beam finite elements are used. Large displacements are accounted for by using the corotational formulation. Structural dynamics is computed by using the Time Discontinuous Galerkin method. Therefore, two different solution procedures are used, one for the fluid domain and the other for the structural part, respectively. These two solvers need to communicate and to transfer each other several information, i.e. stresses, velocities, displacements. In order to guarantee a continuous, effective, and mutual exchange of information, a coupling strategy, consisting of three different algorithms, has been developed and numerically tested. In particular, the effectiveness of the three algorithms is shown in terms of interface energy artificially produced by the approximate fulfilling of compatibility and equilibrium conditions at the fluid-structure interface. The proposed coupled approach is used in order to solve different fluid-structure interaction problems, i.e. cantilever beams immersed in a viscous fluid, the impact of the hull of the ship on the marine free-surface, blood flow in a deformable vessels, and even flapping wings simulating the take-off of a butterfly. The good results achieved in each application highlight the effectiveness of the proposed methodology and of the C++ developed software to successfully approach several two-dimensional fluid-structure interaction problems.

Investigation of the lithium ion mobility in cyclic model compounds and their ion conducting properties

Efficient energy storage and conversion is playing a key role in overcoming the present and future challenges in energy supply. Batteries provide portable, electrochemical storage of green energy sources and potentially allow for a reduction of the dependence on fossil fuels, which is of great importance with respect to the issue of global warming. In view of both, energy density and energy drain, rechargeable lithium ion batteries outperform other present accumulator systems. However, despite great efforts over the last decades, the ideal electrolyte in terms of key characteristics such as capacity, cycle life, and most important reliable safety, has not yet been identified. rnrnSteps ahead in lithium ion battery technology require a fundamental understanding of lithium ion transport, salt association, and ion solvation within the electrolyte. Indeed, well-defined model compounds allow for systematic studies of molecular ion transport. Thus, in the present work, based on the concept of ‘immobilizing’ ion solvents, three main series with a cyclotriphosphazene (CTP), hexaphenylbenzene (HBP), and tetramethylcyclotetrasiloxane (TMS) scaffold were prepared. Lithium ion solvents, among others ethylene carbonate (EC), which has proven to fulfill together with pro-pylene carbonate safety and market concerns in commercial lithium ion batteries, were attached to the different cores via alkyl spacers of variable length.rnrnAll model compounds were fully characterized, pure and thermally stable up to at least 235 °C, covering the requested broad range of glass transition temperatures from -78.1 °C up to +6.2 °C. While the CTP models tend to rearrange at elevated temperatures over time, which questions the general stability of alkoxide related (poly)phosphazenes, both, the HPB and CTP based models show no evidence of core stacking. In particular the CTP derivatives represent good solvents for various lithium salts, exhibiting no significant differences in the ionic conductivity σ_dc and thus indicating comparable salt dissociation and rather independent motion of cations and ions.rnrnIn general, temperature-dependent bulk ionic conductivities investigated via impedance spectroscopy follow a William-Landel-Ferry (WLF) type behavior. Modifications of the alkyl spacer length were shown to influence ionic conductivities only in combination to changes in glass transition temperatures. Though the glass transition temperatures of the blends are low, their conductivities are only in the range of typical polymer electrolytes. The highest σ_dc obtained at ambient temperatures was 6.0 x 10-6 S•cm-1, strongly suggesting a rather tight coordination of the lithium ions to the solvating 2-oxo-1,3-dioxolane moieties, supported by the increased σ_dc values for the oligo(ethylene oxide) based analogues.rnrnFurther insights into the mechanism of lithium ion dynamics were derived from 7Li and 13C Solid- State NMR investigations. While localized ion motion was probed by i.e. 7Li spin-lattice relaxation measurements with apparent activation energies E_a of 20 to 40 kJ/mol, long-range macroscopic transport was monitored by Pulsed-Field Gradient (PFG) NMR, providing an E_a of 61 kJ/mol. The latter is in good agreement with the values determined from bulk conductivity data, indicating the major contribution of ion transport was only detected by PFG NMR. However, the μm-diffusion is rather slow, emphasizing the strong lithium coordination to the carbonyl oxygens, which hampers sufficient ion conductivities and suggests exploring ‘softer’ solvating moieties in future electrolytes.rn

Interacting bosons and fermions in three-dimensional optical lattice potentials

This thesis reports on the realization, characterization and analysis of ultracold bosonic and fermionic atoms in three-dimensional optical lattice potentials. Ultracold quantum gases in optical lattices can be regarded as ideal model systems to investigate quantum many-body physics. In this work interacting ensembles of bosonic 87Rb and fermionic 40K atoms are employed to study equilibrium phases and nonequilibrium dynamics. The investigations are enabled by a versatile experimental setup, whose core feature is a blue-detuned optical lattice that is combined with Feshbach resonances and a red-detuned dipole trap to allow for independent control of tunneling, interactions and external confinement. The Fermi-Hubbard model, which plays a central role in the theoretical description of strongly correlated electrons, is experimentally realized by loading interacting fermionic spin mixtures into the optical lattice. Using phase-contrast imaging the in-situ size of the atomic density distribution is measured, which allows to extract the global compressibility of the many-body state as a function of interaction and external confinement. Thereby, metallic and insulating phases are clearly identified. At strongly repulsive interaction, a vanishing compressibility and suppression of doubly occupied lattice sites signal the emergence of a fermionic Mott insulator. In a second series of experiments interaction effects in bosonic lattice quantum gases are analyzed. Typically, interactions between microscopic particles are described as two-body interactions. As such they are also contained in the single-band Bose-Hubbard model. However, our measurements demonstrate the presence of multi-body interactions that effectively emerge via virtual transitions of atoms to higher lattice bands. These findings are enabled by the development of a novel atom optical measurement technique: In quantum phase revival spectroscopy periodic collapse and revival dynamics of the bosonic matter wave field are induced. The frequencies of the dynamics are directly related to the on-site interaction energies of atomic Fock states and can be read out with high precision. The third part of this work deals with mixtures of bosons and fermions in optical lattices, in which the interspecies interactions are accurately controlled by means of a Feshbach resonance. Studies of the equilibrium phases show that the bosonic superfluid to Mott insulator transition is shifted towards lower lattice depths when bosons and fermions interact attractively. This observation is further analyzed by applying quantum phase revival spectroscopy to few-body systems consisting of a single fermion and a coherent bosonic field on individual lattice sites. In addition to the direct measurement of Bose-Fermi interaction energies, Bose-Bose interactions are proven to be modified by the presence of a fermion. This renormalization of bosonic interaction energies can explain the shift of the Mott insulator transition. The experiments of this thesis lay important foundations for future studies of quantum magnetism with fermionic spin mixtures as well as for the realization of complex quantum phases with Bose-Fermi mixtures. They furthermore point towards physics that reaches beyond the single-band Hubbard model.